Modern motor vehicles currently normally possess a tank ventilation system. In such a system the fuel vapors generated in the fuel tank of the motor vehicle are adsorbed into an active charcoal container. The active charcoal container is connected to the intake tract of the internal combustion engine via a ventilation duct. In the ventilation duct is a tank ventilation valve by means of which the active charcoal container can be connected to or separated from the intake tract, as desired. From time to time the active charcoal container loaded with fuel vapors must be regenerated. To this end, the tank ventilation valve is opened and the adsorbed fuel vapors flow from the active charcoal container into the intake tract and participate in the combustion process of the internal combustion engine. During the regeneration process the active charcoal container is purged by a constant purge stream. However, in this known process the active charcoal container is not optimally regenerated and as a result its adsorption capacity is only partially utilized. The regeneration process must therefore be performed very frequently, which, depending on the operating state of the internal combustion engine, is not always possible.